Problem: You are given an unweighted tree with n vertices. Recall that a tree is a connected undirected graph without cycles.

Your task is to choose three distinct vertices a, b, c on this tree such that the number of edges which belong to at least one of the simple paths between a and b, b and c, or a and c is the maximum possible. See the notes section for a better understanding.

The simple path is the path that visits each vertex at most once.

Input

The first line contains one integer number n (3 ≤ n ≤ 2 ⋅ 10^5) — the number of vertices in the tree. 

Next n - 1 lines describe the edges of the tree in form a_i, b_i (1 ≤ a_i, b_i ≤ n, a_i ≠ b_i). It is guaranteed that given graph is a tree.

Output

In the first line print one integer res — the maximum number of edges which belong to at least one of the simple paths between a and b, b and c, or a and c.

In the second line print three integers a, b, c such that 1 ≤ a, b, c ≤ n and a ≠, b ≠ c, a ≠ c.

If there are several answers, you can print any.

Example

Input


8
1 2
2 3
3 4
4 5
4 6
3 7
3 8


Output


5
1 8 6

Note

The picture corresponding to the first example (and another one correct answer):

<image>

If you choose vertices 1, 5, 6 then the path between 1 and 5 consists of edges (1, 2), (2, 3), (3, 4), (4, 5), the path between 1 and 6 consists of edges (1, 2), (2, 3), (3, 4), (4, 6) and the path between 5 and 6 consists of edges (4, 5), (4, 6). The union of these paths is (1, 2), (2, 3), (3, 4), (4, 5), (4, 6) so the answer is 5. It can be shown that there is no better answer.

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;

public class ThreePathsOnATree {
    ArrayList<Integer>[] adj;
    int[][] maxDistances;
    int[][] maxLeafs;
    int[] result;

    public static void main(String[] args) throws IOException {
        new ThreePathsOnATree().solve();
    }

    public void solve() throws IOException {
        BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(f.readLine());
        this.adj = new ArrayList[n];
        this.maxDistances = new int[n][3];
        this.maxLeafs = new int[n][3];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < 3; j++) {
                maxLeafs[i][j] = i;
            }
        }
        for (int i = 0; i < n; i++) {
            adj[i] = new ArrayList<Integer>();
        }
        for (int i = 0; i < n - 1; i++) {
            StringTokenizer tokenizer = new StringTokenizer(f.readLine());
            int a = Integer.parseInt(tokenizer.nextToken()) - 1;
            int b = Integer.parseInt(tokenizer.nextToken()) - 1;
            this.adj[a].add(b);
            this.adj[b].add(a);
        }

        result = new int[4];

        dfs1(0, -1);
        df2(0, -1);


        System.out.println(this.result[0]);
        System.out.println((this.result[1] + 1) + " " + (this.result[2] + 1) + " " + (result[3] + 1));
    }

    private void dfs1(int node, int parent) {
        PriorityQueue<ValueAndLeaf> pq = new PriorityQueue<ValueAndLeaf>();

        for (int adjacent : adj[node]) {
            if (adjacent == parent) {
                continue;
            }
            dfs1(adjacent, node);
            pq.add(new ValueAndLeaf(this.maxDistances[adjacent][0] + 1, maxLeafs[adjacent][0]));
        }

        for (int i = 0; i < 3; i++) {
            if (!pq.isEmpty()) {
                ValueAndLeaf valueAndLeaf = pq.poll();
                maxDistances[node][i] = valueAndLeaf.value;
                maxLeafs[node][i] = valueAndLeaf.leaf;
            } else {
                maxDistances[node][i] = 0;
                maxLeafs[node][i] = node;
            }
        }

       // System.out.println(node + 1 + " " + this.maxDistances[node][0] + " " + this.maxDistances[node][1] + " " + maxDistances[node][2]);
    }

    private void df2(int node, int parent) {
        PriorityQueue<ValueAndLeaf> pq = new PriorityQueue<ValueAndLeaf>();
        if (parent != -1) {
            if (this.maxLeafs[parent][0] != this.maxLeafs[node][0] && this.maxLeafs[parent][0] != this.maxLeafs[node][1] & this.maxLeafs[parent][0] != this.maxLeafs[node][2]) {
                pq.add(new ValueAndLeaf(this.maxDistances[parent][0] + 1, this.maxLeafs[parent][0]));
            } else {
                pq.add(new ValueAndLeaf(this.maxDistances[parent][1] + 1, this.maxLeafs[parent][1]));
            }
        }
        for (int i = 0; i < 3; i++) {
            pq.add(new ValueAndLeaf(this.maxDistances[node][i], this.maxLeafs[node][i]));
        }

        for (int i = 0; i < 3; i++) {
            if (pq.isEmpty()) break;
            ValueAndLeaf valueAndLeaf = pq.poll();
            maxDistances[node][i] = valueAndLeaf.value;
            maxLeafs[node][i] = valueAndLeaf.leaf;
        }

        if (maxLeafs[node][2] == maxLeafs[node][1]) {
            maxLeafs[node][2] = adj[node].get(0);
        }

        int sum = maxDistances[node][0] + maxDistances[node][1] + maxDistances[node][2];
        //System.out.println(node + 1 + " " + maxDistances[node][0] + " " + maxDistances[node][1] + " " + maxDistances[node][2]);
        if (sum > this.result[0]) {
            this.result[0] = sum;
            for (int i = 1; i <= 3; i++) {
                this.result[i] = this.maxLeafs[node][i - 1];
            }
        }

        for (int adjacent : adj[node]) {
            if (adjacent != parent) {
                df2(adjacent, node);
            }
        }
    }

    private static class ValueAndLeaf implements Comparable<ValueAndLeaf> {
        int value;
        int leaf;

        public ValueAndLeaf(int value, int leaf) {
            this.value = value;
            this.leaf = leaf;
        }

        @Override
        public int compareTo(ValueAndLeaf valueAndLeaf) {
            if (this.value < valueAndLeaf.value) {
                return 1;
            } else if (this.value > valueAndLeaf.value) {
                return -1;
            }

            return 0;
        }
    }
}